We've had no issue with using public campgrounds with our 40' motorhome and Jeep.
Since you're from Colorado I will even say we've spent many, many nights in your state parks.
As full-timers we've also used national parks, national forest campgrounds, Corp of Engineer parks, county and city parks.
So yes, your 32' will not give you any problems. You won't fit in every site but the parks themselves won't be an issue.
I will add - except California's state parks but then there are plenty of other public campgrounds in California and many are much nicer.
